Wayne State University Statistics Worksheet

Sociology 210Winter 2023
Assignment 4 (Due Friday, February 3 at 11:59 pm submitted to Section Canvas.) Use three
significant figures (decimal places) when reporting answers that include decimals.
1 point bonus credit for submitting assignment on-time (not using extension)
A complete answer for probability problems such as those found in Problems 1 and 4 must
include an interpretive sentence relating the probability to the text of the problem in
order to receive full credit.
1. 19 points. The distribution of ACT subject scores is approximately normal with  = 20 and 
= 5. For the population of students who have taken the ACT,
a. 3 points. What proportion of students has ACT scores less than 14?
b. 5 points. What proportion of students has ACT scores between 22 and 28?
c. 3 points. What is the percentile rank of someone who scores 23?
d. 4 points. What is the minimum ACT score needed to be in the 80th percentile?
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e. 4 points. If the state university only accepts students from the top two thirds (66.7%) of
the ACT distribution (meaning they reject the bottom 33.3%), what is the minimum ACT
score needed to be accepted? (HINT: Need to figure out the percentile rank to be in the top
two-thirds, then find Z, then X.)
2. 11 points. The mean height of 9th grade boys at Skyline High School is 5 ft. 8 in. (or 68 in.)
and the standard deviation is 2.25 in. The distribution of heights is approximately Normal.
a. 3 points. Draw a normal probability curve, placing the mean value in its appropriate
place. Also show the x values associated with one, two, and three standard deviations
above and below the mean. Finally, also label the points associated with one, two, and
three standard deviations above and below the mean with their corresponding z-scores.
b. 5 points. Using the normal curve from the previous example and the unit normal table,
what is the probability that a student drawn at random from this population of 9th grade
students will be between 67 and 73 inches tall?
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c. 3 points. What is the probability that a male student drawn at random will be 72 inches
tall or taller?
3. 13 points. The distribution of SAT subject scores is approximately normal with  = 500 and 
= 100. For the population of students who have taken the SAT,
A. 3 points. What proportion of test-takers have SAT scores greater than 720?
B. 3 points. What proportion of test-takers have SAT scores greater than 450?
C. 3 points. What proportion have SAT scores less than 420?
D. 4 points. If the state college only accepts students from the top 33.3% (rejecting the
bottom 66.7%) of the SAT distribution, what is the minimum SAT score needed to be
accepted?
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4. 7 points. From Frankfort and Nachmias (5th edition). You are asked to do a study of
shelters for abused and battered women to determine the necessary capacity in your city to
provide housing for most of these women. Examining the historical data you find that the
mean number of women in shelters each night is 250 with a standard deviation of 50 and that
the distribution of women staying in shelters is approximately Normal.
a. 4 points If the city’s shelters have a capacity of 325, will that be enough places for abused
women on 95% of all nights? If not, what number of shelter openings are needed?
b. 3 points The current capacity is only 225 because some shelters have been closed. What is
the percentage of nights that the number of abused women seeking shelter will exceed the
current capacity?
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